hi,
the rhizomes themselves are not all that thick, they are as thin as grass stems. but they can make a thick mat of themselves immediately under the visible ‘grass’. (i.e. where the rhizomes are in the light they will sprout into grass, where they are in darkness they will be white and stringy.)
if you had only a bit of couch grass you might find some long, white, thin, rhizomes running horizontally but not a mat of the stuff.
but if you have none then i think you will be fine! other UK grasses just give up when covered using charles’ method